Stanford Encyclopedia of Philosophy (2008)

Authors
Leon Horsten
Universität Konstanz
Abstract
If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics
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References found in this work BETA

Aboutness.Stephen Yablo - 2014 - Princeton University Press.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.

View all 82 references / Add more references

Citations of this work BETA

Quantitative Properties.M. Eddon - 2013 - Philosophy Compass 8 (7):633-645.
The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
Mathematical Pluralism.G. Priest - 2013 - Logic Journal of the IGPL 21 (1):4-13.
Intuitionistic epistemic logic.Sergei Artemov & Tudor Protopopescu - 2016 - Review of Symbolic Logic 9 (2):266-298.

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